This article presents a series of numerical simulations of the stratigraphic evolution of continental rift basins. We model the geomorphic and tectonic processes acting in this depositional environment, which contrasts with the traditional approach of modeling the settling of sediments, especially in marine clastic basins. What is new in our model is that it can simulate the formation of basins with linked half grabens, which is a fundamental feature of rift systems.The attributes of the numerical simulations such as the overall morphology, basin architecture, drainage systems, and stratigraphy are in good agreement with digital elevation models and reflection seismic fines of the basins of the East African rift system, specifically the Tanganyika and Malawi rifts.